Thinking Mathematically (6th Edition)

The number of ways in which a series of successive things can occur is found by multiplying the number of ways in which each thing can occur. ------------ You would want to see in how many ways you can choose the 1st letter in the arrangement, the 2nd letter in the arrangement, the 3rd letter in the arrangement, ... the 25th letter in the arrangement, the 26th letter in the arrangement. Since this is a series of successive choices, you would apply the FTC. The answer to the first question is 26. Each successive answer is 1 less than the previous, as we use up each letter once in the arrangement, and the total is 26$\times$25$\times$24$\times$...$\times$3$\times$2$\times$1=26! 10,000 is surpassed with the first three factors, $26\times 25\times 24=15,600.$ and there are another 23 factors... The full number is about 4$\times 10^{26}$ (calculator), which is huge. Does not make sense.